The invention is based on an apparatus for evacuating and closing bag packages as defined hereinafter. In an apparatus of this type known for instance from FIG. 22 of U.S. Pat. No. 2,692,074, the flat top closure fold protruding from the bag package is encompassed by the jaws, and a suction conduit is created between the walls of the closure fold by the application of negative pressure to these walls; through this conduit, the air contained in the package is evacuated by suction. The sealing jaws are movable toward one another between the underside of the jaws and the shoulders of the bag package; after air has been removed by suction, the sealing jaws are pressed together to form a sealed seam at the top closure fold of the bag package. The known evacuating and closing apparatus has a disadvantage that during the evacuation of the bag package, atmospheric air pressure bears on the part of the top closure located between the jaws of the shoulder in the region of the sealing jaws; with negative pressure in the bag package, the two walls of the top closure fold are increasingly pressed together. Because the neck of the bag package is pressed together in this way, only a slight negative pressure can be generated in the bag. The attainable negative pressure depends on the formation of folds and wrinkles in the walls of the top closure of the bag package, and they form small channels through which the air can be removed by suction. However, these channels have a disadvantage that they cannot be sealed off completely during the sealing of the top closure, so that during subsequent storage of the bag packages, air and hence oxygen that damages the product can enter the bag package again.